You could disconnect the wires at the smart button and see what you have then (assuming this is just a doorbell circuit)
Usually the power goes into the chime and they run a switch loop to the button. You should be able to ring the chime straight from the transformer leads. If that doesn't work you have a bad transformer or a bad chime.
I suppose you really should find the transformer and remove it if it is bad or at least remove power from it if it is hanging outside a box, buried in the wall and find an accessible place for a new one.